Question

After well completion, a discovery well in an oil reservoir is produced for a short period and then closed for pressure build-up test. The production history before shut-in is given below. The Horner’s pseudo-producing time, $t_{pH}$, is ............... hr (rounded to nearest integer). 

Production rate (STB/day)	Duration (days)
500	5
550	7
400	8

 

Hint:

For build-up after variable rates, scale each duration by $q_k/q_{\text{last}}$ and sum to get $t_{pH}$ (days), then convert to hours if requested.

Answer 1

Step 1: Horner pseudo-time for variable-rate production.
With last stabilized rate $q_n$ (here $q_n = 400$ STB/day), the equivalent producing time is \[ t_{pH} = \sum_{k} \left(\frac{q_k}{q_n}\right)\Delta t_k \quad \text{(days)}. \] Step 2: Compute in days.
\[ t_{pH} = 5\left(\tfrac{500}{400}\right) + 7\left(\tfrac{550}{400}\right) + 8\left(\tfrac{400}{400}\right) = 6.25 + 9.625 + 8 = 23.875~\text{days}. \] Step 3: Convert to hours and round.
\[ 23.875 \times 24 = 573.0~\text{hr} \;\Rightarrow\; 573~\text{hr (nearest integer)}. \]